Interactive material accompanying the book Indra's Pearls

1. Geometric Transformations

Translation Rotation Spiral Similarity Reflections Inversion

2. Complex Numbers

Complex addition and multiplication (integral) Complex addition and multiplication (generic) Complex conjugation Powers of a complex number

3. Complex transformations

Complex transformations Komplex transformation of a grid (advanced) Geometric transformations as complex functions Iterated geometric transformations

4. Möbius transformations

Möbius transformations Inverse of a Möbius transformation Möbius transformations from the images of three points Möbius transformations from two fixed points Field lines Möbius transformations and stereographic projection

5. Transformation groups

Two translations Dr. Stickler in the hall of mirrors Angled mirrors Kaleidoscopes Wallpaper groups Iterated similarity transformations

6. Iterated function systems

A little foretaste An IFS plant How an IFS is created The role of probabilty IFS from two similarities Barnsley's fern IFS from two Möbius transformations

7. Iterated Möbius Transformations

Two circles Schottky circles Schottky circle dance Limit sets

8. Examples from Indra's Pearls

The ribbon The ribbon with twists The necklace Finishing touches for the necklace Yet another degree of freedom Grandma's recipe